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Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens
, 2012
"... Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). H ..."
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Cited by 104 (34 self)
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Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2012
"... Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion a ..."
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Cited by 19 (5 self)
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Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion as a sparse regression one, under the assumption that the observed image signatures can be expressed as linear combinations of pure spectra, known aprioriand available in a library. It happens, however, that sparse unmixing focuses on analyzing the hyperspectral data without incorporating spatial information. In this paper, we include the total variation (TV) regularization to the classical sparse regression formulation, thus exploiting the spatial– contextual information present in the hyperspectral images and developing a new algorithm called sparse unmixing via variable splitting augmented Lagrangian and TV. Our experimental results, conducted with both simulated and real hyperspectral data sets, indicate the potential of including spatial information (through the TV term) on sparse unmixing formulations for improved characterization of mixed pixels in hyperspectral imagery.
Automated extraction of imagebased endmember bundles for improved spectral unmixing
 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
, 2012
"... Abstract—Spectral unmixing is an important task in hyperspectral data exploitation. It amounts to estimating the abundance of pure spectral constituents (endmembers) in each (possibly mixed) observation collected by the imaging instrument. In recent years, several endmember extraction algorithms (E ..."
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Cited by 8 (3 self)
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Abstract—Spectral unmixing is an important task in hyperspectral data exploitation. It amounts to estimating the abundance of pure spectral constituents (endmembers) in each (possibly mixed) observation collected by the imaging instrument. In recent years, several endmember extraction algorithms (EEAs) have been proposed for automated endmember extraction from hyperspectral data sets. Traditionally, EEAs extract/select only one single standard endmember spectrum for each of the presented endmember classes or scene components. The use of fixed endmember spectra, however, is a simplification since in many cases the conditions of the scene components are spatially and temporally variable. As a result, variation in endmember spectral signatures is not always accounted for and, hence, spectral unmixing can lead to poor accuracy of the estimated endmember fractions. Here, we address this issue by developing a simple strategy to adapt available EEAs to select multiple endmembers (or bundles) per scene component. We run the EEAs in randomly selected subsets of the original hyperspectral image, and group the extracted samples of pure materials in a bundle using a clustering technique. The output is a spectral library of pure materials, extracted automatically from the input scene. The proposed technique is applied to several common EEAs and combined with an endmember variability reduction technique for unmixing purposes. Experiments with both simulated and real hyperspectral data sets indicate that the proposed strategy can significantly improve fractional abundance estimations by accounting for endmember variability in the original hyperspectral data. Index Terms—Endmember extraction algorithms (EEAs), endmember variability, hyperspectral imaging, multiple endmember spectral mixture analysis (MESMA), spectral mixture analysis (SMA). I.
A Sparse Regression Approach to Hyperspectral Unmixing
, 2011
"... Spectral unmixing is an important problem in hyperspectral data exploitation. It amounts at characterizing the mixed spectral signatures collected by an imaging instrument in the form of a combination of pure spectral constituents (endmembers), weighted by their correspondent abundance fractions. Li ..."
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Cited by 6 (0 self)
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Spectral unmixing is an important problem in hyperspectral data exploitation. It amounts at characterizing the mixed spectral signatures collected by an imaging instrument in the form of a combination of pure spectral constituents (endmembers), weighted by their correspondent abundance fractions. Linear spectral unmixing is a popular technique in the literature which assumes linear interactions between the endmembers, thus simplifying the characterization of the mixtures and approaching the problem from a general perspective independent of the physical properties of the observed materials. However, linear spectral unmixing suffers from several shortcomings. First, it is unlikely to find completely pure spectral endmembers in the image data due to spatial resolution and mixture phenomena. Second, the linear mixture model does not naturally include spatial information, which is an important source of information (together with spectral information) to solve the unmixing problem. In this thesis, we propose a completely new approach for spectral unmixing which makes use of spectral libraries of materials collected on the ground or in a laboratory, thus circumventing the problems associated to image endmember extraction. Due to the increasing availability and dimensionality of spectral libraries, this problem calls for efficient sparse regularizers. The resulting approach is called
Intercomparison and validation of techniques for spectral unmixing of hyperspectral images: A planetary case study
 IEEE Transactions on Geoscience and Remote Sensing
, 2011
"... Abstract—As the volume of hyperspectral data for planetary exploration increases, efficient yet accurate algorithms are decisive for their analysis. In this paper, the capability of spectral unmixing for analyzing hyperspectral images from Mars is investigated. For that purpose, we consider the Russ ..."
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Cited by 4 (1 self)
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Abstract—As the volume of hyperspectral data for planetary exploration increases, efficient yet accurate algorithms are decisive for their analysis. In this paper, the capability of spectral unmixing for analyzing hyperspectral images from Mars is investigated. For that purpose, we consider the Russell megadune observed by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) and the HighResolution Imaging Science Experiment (HiRISE) instruments. In late winter, this area of Mars is appropriate for testing linear unmixing techniques because of the geographical coexistence of seasonal CO2 ice and defrosting dusty features that is not resolved by CRISM. Linear unmixing is carried out on a selected CRISM image by seven stateoftheart approaches based on different principles. Three physically coherent sources with an increasing fingerprint of dust are recognized by the majority of the methods. Processing of HiRISE imagery allows the construction of a ground truth in the form of a reference abundance map related to the defrosting features. Validation of abundances estimated by spectral unmixing is carried out in an independent and quantitative manner by comparison with the ground truth. The quality of the results is estimated through the correlation coefficient and average error between the reconstructed and reference abundance maps. Intercomparison of the selected linear unmixing approaches is performed. Global and local comparisons show that misregistration inaccuracies between the HiRISE and CRISM images represent the major source of error. We also conclude that abundance maps provided by three methods out of seven are generally accurate, i.e., sufficient for a planetary interpretation.
ACCURACY AND PERFORMANCE OF LINEAR UNMIXING TECHNIQUES FOR DETECTING MINERALS ON OMEGA/MARS EXPRESS
"... Detecting minerals on a huge hyperspectral dataset (> To) is a difficult task that we proposed to address using linear unmixing techniques. We test different algorithms with positivity constrains on a typical Martian hyperspectral image of the Syrtis Major volcanic complex. The usefulness of addi ..."
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Detecting minerals on a huge hyperspectral dataset (> To) is a difficult task that we proposed to address using linear unmixing techniques. We test different algorithms with positivity constrains on a typical Martian hyperspectral image of the Syrtis Major volcanic complex. The usefulness of additional constrains, such as sparsity and sumtoone constrains are discussed. We compare the results with a supervised detection technique based on band ratio. Index Terms — Hyperspectral imaging, supervised classification, linear unmixing, positivity, sumtoone,
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"... Accuracy and performance of linear unmixing techniques for detecting minerals on OMEGA/MEx ..."
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Accuracy and performance of linear unmixing techniques for detecting minerals on OMEGA/MEx
MultiImage Unsupervised Spectral Analysis
"... Large data sets delivered by imaging spectrometers are interesting in many ways in the Planetary Sciences. Due to the size of the data, which often prohibits conventional exploratory data analysis, unsupervised analysis methods could be a way of gathering interesting information contained in the dat ..."
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Large data sets delivered by imaging spectrometers are interesting in many ways in the Planetary Sciences. Due to the size of the data, which often prohibits conventional exploratory data analysis, unsupervised analysis methods could be a way of gathering interesting information contained in the data. In this work, we investigate some of the opportunities and limitations of unsupervised analysis based on nonnegative matrix approximation [2] in planetary settings. Since typically there often is no ground truth to compare to, unsupervised rather than supervised methods allow to extract new information from data sets. Often, the practicability of these methods suffered from low performance, which made largescale analyses almost prohibitively
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"... This article presents a comparative study of three different types of estimators used for supervised linear unmixing of a MEx/OMEGA hyperspectral cube. The algorithms take into account the constraints of the abundance fractions, so as to get physically interpretable results. Abundance and spatial re ..."
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This article presents a comparative study of three different types of estimators used for supervised linear unmixing of a MEx/OMEGA hyperspectral cube. The algorithms take into account the constraints of the abundance fractions, so as to get physically interpretable results. Abundance and spatial reconstruction error maps show that using a Bayesian MAP estimator, a satisfying compromise between complexity and performance can be achieved. 1.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Geometric Unmixing of Large Hyperspectral Images: A Barycentric Coordinate Approach
"... Abstract—In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques hav ..."
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Abstract—In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques have been proposed in literature, based on either a statistical or a geometrical formulation. However, most, if not all, of these techniques for estimating abundances use a leastsquares solution. In this paper, we show that abundances can be estimated using a geometric formulation. To this end, we express abundances with the barycentric coordinates in the simplex defined by endmembers. We propose to write them in terms of a ratio of volumes or a ratio of distances, which are quantities that are often computed to identify endmembers. This property allows us to easily incorporate abundance estimation within conventional endmember extraction techniques, without incurring additional computational complexity. We use this key property with various endmember extraction techniques, such as NFindr, vertex component analysis, simplex growing algorithm, and iterated constrained endmembers. The relevance of the method is illustrated with experimental results on real hyperspectral images. Index Terms—Abundance estimation, Cramer’s rule, endmember extraction, hyperspectral image, iterated constrained endmembers algorithm, NFindr, orthogonal subspace projection, simplex, simplex growing algorithm, unmixing spectral data, vertex component analysis. I.